Noncrossing quantile regression curve estimation

Abstract

SUMMARYSince quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution for the response. A simple constrained version of quantile regression is proposed to avoid the crossing problem for both linear and nonparametric quantile curves. A simulation study and a reanalysis of tropical cyclone intensity data shows the usefulness of the procedure. Asymptotic properties of the estimator are equivalent to the typical approach under standard conditions, and the proposed estimator reduces to the classical one if there is no crossing. The performance of the constrained estimator has shown significant improvement by adding smoothing and stability across the quantile levels.

Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression

“…However, as the conditional quantiles at different levels α 1 and α 2 are estimated independently it can occur that for given covariate realizations and levels α 1 < α 2 , q α 1 can have a larger value than q α 2 , an effect known as quantile crossing. Whereas different approaches have already been proposed to combat quantile crossing, see, e.g., He (1997), Dette and Volgushev (2008) or Bondell et al (2010), the novel D-vine copula based quantile regression of Kraus and Czado (2017a) also ensures that this effect is prevented.…”

Reconsidering the Income-Illness Relationship Using Distributional Regression An Application to Germany

“…Since their proposition by Koenker and Bassett (1978), quantiles have enjoyed a growing popularity and numerous extensions have been proposed (see among others Bondell et al, 2010;Galvao et al, 2013;Waldmann et al, 2013). Quantile regression allows for the estimation of conditional quantiles, i.e.…”

The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective

“…If quantiles cross, corrections must be applied to obtain a valid conditional distribution of volatility. For instance, to cope with the crossing problem, Koenker [43] applied parallel quantile planes, whereas Bondell et al [44] estimated the quantile regression coefficients with a constrained optimization method. Here, we follow a different approach proposed by Zhao [45].…”